Introduction to Meridian Demo (JAX Backend)

    Welcome to the Meridian end-to-end demo using the JAX backend. This simplified demo showcases the fundamental functionalities and basic usage of the library using JAX for faster and more efficient modeling. It includes working examples of the major modeling steps:

    1. Install and Environment Configuration
    2. Load the data
    3. Configure the model
    4. Run post-modeling quality checks
    5. Run model diagnostics
    6. Generate model results & two-page output
    7. Run budget optimization & two-page output
    8. Save the model object
    9. Interactive Scenario Planning

    Note that this notebook skips all of the exploratory data analysis and preprocessing steps. It assumes that you have completed these tasks before reaching this point in the demo.

    This notebook utilizes sample data. As a result, the numbers and results obtained might not accurately reflect what you encounter when working with a real dataset.

    Step 0: Install and Enviroment Configuration

    1. Make sure you are using one of the available GPU Colab runtimes which is requiredto run Meridian. You can change your notebook's runtime in Runtime > Change runtime type in the menu. All users can use the T4 GPU runtime which is sufficient to run the demo colab, free of charge. Users who have purchased one of Colab's paid plans have access to premium GPUs (such as V100, A100 or L4 Nvidia GPU).

    2. Install the latest version of Meridian, and verify that GPU is available.

      # Uninstall TensorFlow, it is not needed when running Meridian with JAX. 
 
 pip  
uninstall  
tensorflow  
-y  
-q 

      # Install meridian: from PyPI @ latest release 
 
 pip  
install  
--upgrade  
google-meridian [ 
colab,and-cuda,schema ] 
 
  
  # Install meridian: from PyPI @ specific version 
 
  # !pip install google-meridian[colab,and-cuda,schema]==1.3.1 
 
  
  # Install meridian: from GitHub @HEAD 
 
  # !pip install --upgrade "google-meridian[colab,and-cuda,schema] @ git+https://github.com/google/meridian.git@main" 
 

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Using cached tensorflow-2.20.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (620.7 MB)
Installing collected packages&colon; tensorflow
ERROR&colon; pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
tensorflow-decision-forests 1.12.0 requires tensorflow==2.19.0, but you have tensorflow 2.20.0 which is incompatible.
tensorflow-text 2.19.0 requires tensorflow<2.20,>=2.19.0, but you have tensorflow 2.20.0 which is incompatible.
Successfully installed tensorflow-2.20.0
     
      import 
  
 os 
 # This needs to be set prior to meridian import. 
 os 
 . 
 environ 
 [ 
 'MERIDIAN_BACKEND' 
 ] 
 = 
 'jax' 
 

      import 
  
 IPython 
 from 
  
 meridian 
  
 import 
 constants 
 from 
  
 meridian.analysis 
  
 import 
 analyzer 
 from 
  
 meridian.analysis 
  
 import 
 optimizer 
 from 
  
 meridian.analysis 
  
 import 
 summarizer 
 from 
  
 meridian.analysis 
  
 import 
 visualizer 
 from 
  
 meridian.analysis.review 
  
 import 
 reviewer 
 from 
  
 meridian.data 
  
 import 
 data_frame_input_data_builder 
 from 
  
 meridian.model 
  
 import 
 model 
 from 
  
 meridian.model 
  
 import 
 prior_distribution 
 from 
  
 meridian.model 
  
 import 
 spec 
 from 
  
 meridian.schema.serde 
  
 import 
 meridian_serde 
 import 
  
 numpy 
  
 as 
  
 np 
 import 
  
 pandas 
  
 as 
  
 pd 
 # check if GPU is available 
 from 
  
 psutil 
  
 import 
 virtual_memory 
 import 
  
 jax 
 import 
  
 jax.numpy 
  
 as 
  
 jnp 
 # Use jax.numpy instead of tensorflow 
 import 
  
 tensorflow_probability 
  
 as 
  
 tfp 
 tfp_jax 
 = 
 tfp 
 . 
 substrates 
 . 
 jax 
 ram_gb 
 = 
 virtual_memory 
 () 
 . 
 total 
 / 
 1e9 
 print 
 ( 
 'Your runtime has 
 {:.1f} 
 gigabytes of available RAM 
 \n 
 ' 
 . 
 format 
 ( 
 ram_gb 
 )) 
 print 
 ( 
 'Num GPUs Available: ' 
 , 
 len 
 ([ 
 d 
 for 
 d 
 in 
 jax 
 . 
 devices 
 () 
 if 
 d 
 . 
 platform 
 == 
 'gpu' 
 ]), 
 ) 
 print 
 ( 
 'Num CPUs Available: ' 
 , 
 len 
 ([ 
 d 
 for 
 d 
 in 
 jax 
 . 
 devices 
 () 
 if 
 d 
 . 
 platform 
 == 
 'cpu' 
 ]), 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/meridian/backend/config.py&colon;68&colon; UserWarning&colon; The JAX backend is currently under development and is not yet functional. It is intended for internal testing only and should not be used. Please use the TensorFlow backend.
  _warn_jax_experimental()
Your runtime has 13.6 gigabytes of available RAM

Num GPUs Available&colon;  1
Num CPUs Available&colon;  0

    3. Mount a storage. Use meridian_root to refer the mounted root. The mounted root will be used to save trained model , stage two-pager output and generate scenario planning dashboard .

    For Colab Free/Pro user, we will use the MyDrive folder in Google Drive as the external storage. For Colab Enterprise user, we will use Cloud FUSE to mount a GCS bucket.

      # @markdown If you are using Colab Free, Colab Pro, run this cell to mount your Google Drive. 
 from 
  
 google.colab 
  
 import 
 drive 
 drive_mount 
 = 
 '/content/drive' 
 drive 
 . 
 mount 
 ( 
 drive_mount 
 , 
 force_remount 
 = 
 True 
 ) 
 subfolder 
 = 
 '' 
 # @param {"type":"string","placeholder": "Optional, specifying a subfolder is recommended for organizing distinct execution runs."} 
 # Change this "MyDrive" to other share folders name if you would like to use a different drive. 
 meridian_root 
 = 
 f 
 ' 
 { 
 drive_mount 
 } 
 /MyDrive/ 
 { 
 subfolder 
 } 
 ' 
 is_enterprise_user 
 = 
 False 
 

    Mounted at /content/drive
     

      # @markdown If you are using Colab Enterprise, uncomment and run this cell to mount a GCS bucket. 
 # import os 
 # project_id = ""# @param {"type":"string","placeholder": "Cloud project id"} 
 # bucket_name = "" # @param {"type":"string","placeholder": "GCS bucket that contains your model"} 
 # subfolder = "" # @param {"type":"string","placeholder": "Optional, specifying a subfolder is recommended for organizing distinct execution runs."} 
 # os.environ['GOOGLE_CLOUD_PROJECT'] = project_id 
 # !gcloud config set project {project_id} 
 # !gcloud auth login 
 # !mkdir /content/{bucket_name} 
 # # Uncomment below if you don't have gcsfuse installed 
 # #!echo "deb https://packages.cloud.google.com/apt gcsfuse-`lsb_release -c -s` main" | sudo tee /etc/apt/sources.list.d/gcsfuse.list 
 # #!curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | sudo apt-key add - 
 # #!apt-get update 
 # #!apt-get install gcsfuse 
 # !gcsfuse --implicit-dirs {bucket_name} /content/{bucket_name} 
 # meridian_root = f'/content/{bucket_name}/{subfolder}' 
 # is_enterprise_user=True 
 #!fusermount -u /content/{bucket_name}

    Step 1: Load the data

    Load the simulated dataset in CSV format as follows.

    1. Read the data into a Pandas DataFrame.

      df 
 = 
 pd 
 . 
 read_csv 
 ( 
 # Optionally, use `f"${meridian_root}/<path_to_csv>"` to load data from the mounted storage. 
 "https://raw.githubusercontent.com/google/meridian/refs/heads/main/meridian/data/simulated_data/csv/geo_all_channels.csv" 
 )

    2. Create a DataFrameInputDataBuilder instance.

      builder 
 = 
 data_frame_input_data_builder 
 . 
 DataFrameInputDataBuilder 
 ( 
 kpi_type 
 = 
 'non_revenue' 
 , 
 default_kpi_column 
 = 
 'conversions' 
 , 
 default_revenue_per_kpi_column 
 = 
 'revenue_per_conversion' 
 , 
 )

    3. Offer the components to the builder. Note that the components may be offered all at once or piecewise.

      builder 
 = 
 ( 
 builder 
 . 
 with_kpi 
 ( 
 df 
 ) 
 . 
 with_revenue_per_kpi 
 ( 
 df 
 ) 
 . 
 with_population 
 ( 
 df 
 ) 
 . 
 with_controls 
 ( 
 df 
 , 
 control_cols 
 = 
 [ 
 "sentiment_score_control" 
 , 
 "competitor_sales_control" 
 ] 
 ) 
 ) 
 channels 
 = 
 [ 
 "Channel0" 
 , 
 "Channel1" 
 , 
 "Channel2" 
 , 
 "Channel3" 
 , 
 "Channel4" 
 ] 
 builder 
 = 
 builder 
 . 
 with_media 
 ( 
 df 
 , 
 media_cols 
 = 
 [ 
 f 
 " 
 { 
 channel 
 } 
 _impression" 
 for 
 channel 
 in 
 channels 
 ], 
 media_spend_cols 
 = 
 [ 
 f 
 " 
 { 
 channel 
 } 
 _spend" 
 for 
 channel 
 in 
 channels 
 ], 
 media_channels 
 = 
 channels 
 , 
 )
    1. If your data includes organic media or non-media treatments, you can add them using with_organic_media and with_non_media_treatments methods. For the definition of each variable, see Collect and organize your data 
      builder 
 = 
 builder 
 . 
 with_non_media_treatments 
 ( 
 df 
 , 
 non_media_treatment_cols 
 = 
 [ 
 'Promo' 
 ] 
 ) 
 . 
 with_organic_media 
 ( 
 df 
 , 
 organic_media_cols 
 = 
 [ 
 'Organic_channel0_impression' 
 ], 
 organic_media_channels 
 = 
 [ 
 'Organic_channel0' 
 ], 
 )
    1. Finally, build the InputData.
      data 
 = 
 builder 
 . 
 build 
 ()

    Note that the simulated data here does not contain reach and frequency. We recommend including reach and frequency data whenever they are available. For information about the advantages of utilizing reach and frequency, see Bayesian Hierarchical Media Mix Model Incorporating Reach and Frequency Data . For code snippet for loading reach and frequency data, see Load geo-level data with reach and frequency

    The documentation provides guidance for instances where reach and frequency data is accessible for specific channels. Additionally, for information about how to load other data types and formats, including data with reach and frequency, see Supported data types and formats .

    Step 2: Configure the model

    Meridian uses Bayesian framework and Markov Chain Monte Carlo (MCMC) algorithms to sample from the posterior distribution.

    1. Inititalize the Meridian class by passing the loaded data and the customized model specification. One advantage of Meridian lies in its capacity to calibrate the model directly through ROI priors, as described in Media Mix Model Calibration With Bayesian Priors . In this particular example, the ROI priors for all media channels are identical, with each being represented as Lognormal(0.2, 0.9).

      roi_mu 
 = 
 0.2 
 # Mu for ROI prior for each media channel. 
 roi_sigma 
 = 
 0.9 
 # Sigma for ROI prior for each media channel. 
 prior 
 = 
 prior_distribution 
 . 
 PriorDistribution 
 ( 
 roi_m 
 = 
 tfp_jax 
 . 
 distributions 
 . 
 LogNormal 
 ( 
 roi_mu 
 , 
 roi_sigma 
 , 
 name 
 = 
 constants 
 . 
 ROI_M 
 ) 
 ) 
 model_spec 
 = 
 spec 
 . 
 ModelSpec 
 ( 
 prior 
 = 
 prior 
 , 
 enable_aks 
 = 
 True 
 ) 
 mmm 
 = 
 model 
 . 
 Meridian 
 ( 
 input_data 
 = 
 data 
 , 
 model_spec 
 = 
 model_spec 
 )

    2. Use the sample_prior() and sample_posterior() methods to obtain samples from the prior and posterior distributions of model parameters. If you are using the T4 GPU runtime this step may take about 10 minutes for the provided data set.

      %% 
 time 
 mmm 
 . 
 sample_prior 
 ( 
 500 
 ) 
 mmm 
 . 
 sample_posterior 
 ( 
 n_chains 
 = 
 10 
 , 
 n_adapt 
 = 
 2500 
 , 
 n_burnin 
 = 
 500 
 , 
 n_keep 
 = 
 1000 
 , 
 seed 
 = 
 0 
 , 
 unrolled_leapfrog_steps 
 = 
 5 
 , 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/meridian/model/knots.py&colon;505&colon; RuntimeWarning&colon; overflow encountered in cast
  np.float32(math.comb(ncol, design_mat.shape[1]))
CPU times&colon; user 9min 42s, sys&colon; 31.4 s, total&colon; 10min 13s
Wall time&colon; 10min 8s
/usr/local/lib/python3.12/dist-packages/arviz/data/inference_data.py&colon;157&colon; UserWarning&colon; trace group is not defined in the InferenceData scheme
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/arviz/data/inference_data.py&colon;1647&colon; UserWarning&colon; trace group is not defined in the InferenceData scheme
  warnings.warn(

    For more information about configuring the parameters and using a customized model specification, such as setting different ROI priors for each media channel, see Configure the model .

    Step 3: Run post-modeling health checks

    These post-modeling health checks are designed to diagnose common issues related to model convergence, specification, and plausibility. Run the following command to generate the results for all necessary diagnostics:

      health_summary 
 = 
 reviewer 
 . 
 ModelReviewer 
 ( 
 mmm 
 ) 
 . 
 run 
 () 
 filename 
 = 
 'health_card.html' 
 health_summary 
 . 
 output_model_health_card 
 ( 
 filename 
 = 
 filename 
 , 
 filepath 
 = 
 meridian_root 
 ) 
 IPython 
 . 
 display 
 . 
 HTML 
 ( 
 filename 
 = 
 f 
 ' 
 { 
 meridian_root 
 }{ 
 filename 
 } 
 ' 
 )

    Step 4: Run model diagnostics

    To further assess convergence and model fit, you can use the methods from visualizer module.

    1. Assess convergence. Run the following code to generate r-hat statistics. R-hat close to 1.0 indicate convergence. R-hat < 1.2 indicates approximate convergence and is a reasonable threshold for many problems.

      model_diagnostics 
 = 
 visualizer 
 . 
 ModelDiagnostics 
 ( 
 mmm 
 ) 
 model_diagnostics 
 . 
 plot_rhat_boxplot 
 ()

    2. Assess the model's fit by comparing the expected sales against the actual sales.

      model_fit 
 = 
 visualizer 
 . 
 ModelFit 
 ( 
 mmm 
 ) 
 model_fit 
 . 
 plot_model_fit 
 ()

    For more information and additional model diagnostics checks, see Modeling diagnostics .

    Step 5: Generate model results & two-page output

    To export the two-page HTML summary output, initialize the Summarizer class with the model object. Then pass in the filename, filepath, start date, and end date to output_model_results_summary to run the summary for that time duration and save it to the specified file.

      mmm_summarizer 
 = 
 summarizer 
 . 
 Summarizer 
 ( 
 mmm 
 ) 
 

      filepath 
 = 
 meridian_root 
 start_date 
 = 
 '2021-01-25' 
 end_date 
 = 
 '2024-01-15' 
 mmm_summarizer 
 . 
 output_model_results_summary 
 ( 
 'summary_output.html' 
 , 
 filepath 
 , 
 start_date 
 , 
 end_date 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/numpy/lib/_function_base_impl.py&colon;4779&colon; RuntimeWarning&colon; invalid value encountered in subtract
  diff_b_a = subtract(b, a)
/usr/local/lib/python3.12/dist-packages/meridian/analysis/analyzer.py&colon;3352&colon; UserWarning&colon; Effectiveness is not reported because it does not have a clear interpretation by time period.
  warnings.warn(

    Here is a preview of the two-page output based on the simulated data:

      IPython 
 . 
 display 
 . 
 HTML 
 ( 
 filename 
 = 
 f 
 ' 
 { 
 meridian_root 
 } 
 /summary_output.html' 
 )

    For a customized two-page report, model results summary table, and individual visualizations, see Model results report and plot media visualizations .

    Step 6: Run budget optimization & generate an optimization report

    You can choose what scenario to run for the budget allocation. In default scenario, you find the optimal allocation across channels for a given budget to maximize the return on investment (ROI).

    Alternatively, if you would like to have a sharable interactive dashboard, check out Meridian Scenario Planner .

    1. Instantiate the BudgetOptimizer class and run the optimize() method without any customization, to run the default library's Fixed Budget Scenario to maximize ROI.

      %% 
 time 
 budget_optimizer 
 = 
 optimizer 
 . 
 BudgetOptimizer 
 ( 
 mmm 
 ) 
 optimization_results 
 = 
 budget_optimizer 
 . 
 optimize 
 () 
 

    CPU times&colon; user 28.2 s, sys&colon; 2.13 s, total&colon; 30.3 s
Wall time&colon; 32.6 s

    2. Export the 2-page HTML optimization report, which contains optimized spend allocations and ROI.

      filepath 
 = 
 meridian_root 
 optimization_results 
 . 
 output_optimization_summary 
 ( 
 'optimization_output.html' 
 , 
 filepath 
 ) 
 

      IPython 
 . 
 display 
 . 
 HTML 
 ( 
 filename 
 = 
 f 
 ' 
 { 
 meridian_root 
 } 
 /optimization_output.html' 
 )

    For information about customized optimization scenarios, such as flexible budget scenarios, see Budget optimization scenarios . For more information about optimization results summary and individual visualizations, see optimization results output and optimization visualizations .

    Optimization can also be performed on a hypothetical data representing a future scenario. The new data takes the same structure as the input data and encodes an anticipated flighting pattern, cost per media unit, and revenue per kpi.

    3. Load the simulated dataset in CSV format into Pandas DataFrame.

      df 
 = 
 pd 
 . 
 read_csv 
 ( 
 "https://raw.githubusercontent.com/google/meridian/refs/heads/main/meridian/data/simulated_data/csv/hypothetical_geo_all_channels.csv" 
 )

    4. New data is read from a csv file and converted into a set of multi-dimensional arrays. The arrays are used to construct a DataTensors instance, which is passed to optimize() as the new_data argument.

    Constructing a DataTensors instance requires that all arrays have "time" and "geo" dimensions. Alternatively, the BudgetOptimizer.create_optimization_tensors method can be used to construct a DataTensors instance. This helper method can simplify the process, particularly when you do not need "time" and "geo" dimensions for all inputs. For example, it can be convenient if you want to assume a constant "revenue per kpi" or "cost per media unit" for all geos and time periods.

      n_geos 
 = 
 mmm 
 . 
 n_geos 
 n_media_channels 
 = 
 mmm 
 . 
 n_media_channels 
 n_non_media_channels 
 = 
 mmm 
 . 
 n_non_media_channels 
 n_organic_media_channels 
 = 
 mmm 
 . 
 n_organic_media_channels 
 # The number of time periods and time range do not need to match the input data. 
 df 
 [ 
 constants 
 . 
 TIME 
 ] 
 = 
 pd 
 . 
 to_datetime 
 ( 
 df 
 [ 
 constants 
 . 
 TIME 
 ], 
 errors 
 = 
 'coerce' 
 ) 
 unique_times 
 = 
 sorted 
 ( 
 df 
 [ 
 constants 
 . 
 TIME 
 ] 
 . 
 unique 
 ()) 
 n_times 
 = 
 len 
 ( 
 unique_times 
 ) 
 geos 
 = 
 mmm 
 . 
 input_data 
 . 
 geo 
 . 
 values 
 media_channels 
 = 
 mmm 
 . 
 input_data 
 . 
 media_channel 
 . 
 values 
 media_cols 
 = 
 [ 
 f 
 " 
 { 
 channel 
 } 
 _impression" 
 for 
 channel 
 in 
 media_channels 
 ] 
 media_spend_cols 
 = 
 [ 
 f 
 " 
 { 
 channel 
 } 
 _spend" 
 for 
 channel 
 in 
 media_channels 
 ] 
 non_media_treatment_cols 
 = 
 [ 
 'Promo' 
 ] 
 organic_media_cols 
 = 
 [ 
 'Organic_channel0_impression' 
 ] 
 organic_media_channels 
 = 
 [ 
 'Organic_channel0' 
 ] 
 revenue_per_kpi_col 
 = 
 'revenue_per_conversion' 
 times_str 
 = 
 [ 
 time 
 . 
 strftime 
 ( 
 constants 
 . 
 DATE_FORMAT 
 ) 
 for 
 time 
 in 
 unique_times 
 ] 
 media_np 
 = 
 np 
 . 
 zeros 
 (( 
 n_geos 
 , 
 n_times 
 , 
 n_media_channels 
 )) 
 media_spend_np 
 = 
 np 
 . 
 zeros 
 (( 
 n_geos 
 , 
 n_times 
 , 
 n_media_channels 
 )) 
 non_media_treatment_np 
 = 
 np 
 . 
 zeros 
 (( 
 n_geos 
 , 
 n_times 
 , 
 n_non_media_channels 
 )) 
 organic_media_np 
 = 
 np 
 . 
 zeros 
 (( 
 n_geos 
 , 
 n_times 
 , 
 n_organic_media_channels 
 )) 
 revenue_per_kpi_np 
 = 
 np 
 . 
 zeros 
 (( 
 n_geos 
 , 
 n_times 
 )) 
 df_grouped 
 = 
 df 
 . 
 set_index 
 ([ 
 constants 
 . 
 GEO 
 , 
 constants 
 . 
 TIME 
 ]) 
 for 
 geo_idx 
 , 
 geo 
 in 
 enumerate 
 ( 
 geos 
 ): 
 for 
 time_idx 
 , 
 time 
 in 
 enumerate 
 ( 
 unique_times 
 ): 
 row 
 = 
 df_grouped 
 . 
 loc 
 [( 
 geo 
 , 
 time 
 )] 
 media_np 
 [ 
 geo_idx 
 , 
 time_idx 
 , 
 :] 
 = 
 row 
 [ 
 media_cols 
 ] 
 . 
 values 
 media_spend_np 
 [ 
 geo_idx 
 , 
 time_idx 
 , 
 :] 
 = 
 row 
 [ 
 media_spend_cols 
 ] 
 . 
 values 
 non_media_treatment_np 
 [ 
 geo_idx 
 , 
 time_idx 
 , 
 :] 
 = 
 row 
 [ 
 non_media_treatment_cols 
 ] 
 . 
 values 
 organic_media_np 
 [ 
 geo_idx 
 , 
 time_idx 
 , 
 :] 
 = 
 row 
 [ 
 organic_media_cols 
 ] 
 . 
 values 
 revenue_per_kpi_np 
 [ 
 geo_idx 
 , 
 time_idx 
 ] 
 = 
 row 
 [ 
 revenue_per_kpi_col 
 ] 
 . 
 item 
 () 
 data_tensors 
 = 
 analyzer 
 . 
 DataTensors 
 ( 
 media 
 = 
 jnp 
 . 
 array 
 ( 
 media_np 
 , 
 dtype 
 = 
 jnp 
 . 
 float32 
 ), 
 media_spend 
 = 
 jnp 
 . 
 array 
 ( 
 media_spend_np 
 , 
 dtype 
 = 
 jnp 
 . 
 float32 
 ), 
 non_media_treatments 
 = 
 jnp 
 . 
 array 
 ( 
 non_media_treatment_np 
 , 
 dtype 
 = 
 jnp 
 . 
 float32 
 ), 
 organic_media 
 = 
 jnp 
 . 
 array 
 ( 
 organic_media_np 
 , 
 dtype 
 = 
 jnp 
 . 
 float32 
 ), 
 revenue_per_kpi 
 = 
 jnp 
 . 
 array 
 ( 
 revenue_per_kpi_np 
 , 
 dtype 
 = 
 jnp 
 . 
 float32 
 ), 
 time 
 = 
 times_str 
 , 
 ) 
 # Default values for `budget` and `pct_of_spend` are derived from the `new_data`, 
 # but these values can be overridden without modifying the `new_data` itself. 
 hypothetical_optimization_results 
 = 
 budget_optimizer 
 . 
 optimize 
 ( 
 new_data 
 = 
 data_tensors 
 , 
 budget 
 = 
 50_000_000 
 , 
 pct_of_spend 
 = 
 [ 
 .2 
 , 
 .1 
 , 
 .2 
 , 
 .2 
 , 
 .3 
 ] 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/meridian/analysis/analyzer.py&colon;397&colon; UserWarning&colon; A `organic_media` value was passed in the `new_data` argument. This is not supported and will be ignored.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/meridian/analysis/analyzer.py&colon;397&colon; UserWarning&colon; A `non_media_treatments` value was passed in the `new_data` argument. This is not supported and will be ignored.
  warnings.warn(

    5. Export the 2-page HTML optimization report.

      filepath 
 = 
 meridian_root 
 hypothetical_optimization_results 
 . 
 output_optimization_summary 
 ( 
 'hypothetical_optimization_output.html' 
 , 
 filepath 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/meridian/analysis/analyzer.py&colon;397&colon; UserWarning&colon; A `organic_media` value was passed in the `new_data` argument. This is not supported and will be ignored.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/meridian/analysis/analyzer.py&colon;397&colon; UserWarning&colon; A `non_media_treatments` value was passed in the `new_data` argument. This is not supported and will be ignored.
  warnings.warn(
     
      IPython 
 . 
 display 
 . 
 HTML 
 ( 
 filename 
 = 
 f 
 ' 
 { 
 meridian_root 
 } 
 /hypothetical_optimization_output.html' 
 )

    Step 7: Save the model object

    We recommend that you save the model object for future use. This helps you to avoid repetitive model runs and saves time and computational resources. After the model object is saved, you can load it at a later stage to continue the analysis or visualizations without having to re-run the model.

    Run the following codes to save the model object:

      file_path 
 = 
 f 
 ' 
 { 
 meridian_root 
 } 
 /saved_mmm.binpb' 
 meridian_serde 
 . 
 save_meridian 
 ( 
 mmm 
 , 
 file_path 
 ) 
 print 
 ( 
 f 
 'model is saved at 
 { 
 file_path 
 } 
 ' 
 ) 
 

    model is saved at /content/drive/MyDrive//saved_mmm.binpb

    Run the following codes to load the saved model:

      mmm 
 = 
 meridian_serde 
 . 
 load_meridian 
 ( 
 file_path 
 ) 
 

    /usr/local/lib/python3.12/dist-packages/meridian/schema/utils/proto_enum_converter.py&colon;105&colon; UserWarning&colon; Paid media prior type is unspecified. Resolving to default&colon; PAID_MEDIA_PRIOR_TYPE_UNSPECIFIED.
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/arviz/data/inference_data.py&colon;1538&colon; UserWarning&colon; The group trace is not defined in the InferenceData scheme
  warnings.warn(
/usr/local/lib/python3.12/dist-packages/meridian/model/knots.py&colon;505&colon; RuntimeWarning&colon; overflow encountered in cast
  np.float32(math.comb(ncol, design_mat.shape[1]))
     

      # @markdown If a GCS bucket is mounted, run this cell to unmount it. 
 
 fusermount  
-u  
/content/ { 
bucket_name } 
 

    fusermount&colon; failed to unmount /content/{bucket_name}&colon; No such file or directory

    Step 8: Interactive Scenario Planning

    Meridian Scenario Planner is a tool that allow advertisers to create a sharable and interactive dashboard from Colab; you can reuse the saved model from this Colab for dashboard generation.

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